Compressing audio waveforms using neural networks and vector quantizers

ABSTRACT

Methods, systems and apparatus, including computer programs encoded on computer storage media. One of the methods includes receiving an audio waveform that includes a respective audio sample for each of a plurality of time steps, processing the audio waveform using an encoder neural network to generate a plurality of feature vectors representing the audio waveform, generating a respective coded representation of each of the plurality of feature vectors using a plurality of vector quantizers that are each associated with a respective codebook of code vectors, wherein the respective coded representation of each feature vector identifies a plurality of code vectors, including a respective code vector from the codebook of each vector quantizer, that define a quantized representation of the feature vector, and generating a compressed representation of the audio waveform by compressing the respective coded representation of each of the plurality of feature vectors.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. application Ser. No. 17/856,856, filed onJul. 1, 2022, which claims priority to U.S. Provisional Application No.63/218,139, filed on Jul. 2, 2021. The disclosures of the priorapplications are considered part of and are incorporated by reference inthe disclosure of this application.

BACKGROUND

This specification relates to processing data using machine learningmodels.

Machine learning models receive an input and generate an output, e.g., apredicted output, based on the received input. Some machine learningmodels are parametric models and generate the output based on thereceived input and on values of the parameters of the model.

Some machine learning models are deep models that employ multiple layersof models to generate an output for a received input. For example, adeep neural network is a deep machine learning model that includes anoutput layer and one or more hidden layers that each apply a non-lineartransformation to a received input to generate an output.

SUMMARY

This specification generally describes a compression system implementedas computer programs on one or more computers in one or more locationsthat can compress audio waveforms. The specification further describes adecompression system implemented as computer programs on one or morecomputers in one or more locations that can decompress audio waveforms.

Generally, the compression system and the decompression system can belocated in any appropriate locations. In particular, the compressionsystem can optionally be located remotely from the decompression system.For example, the compression system can be implemented by one or morefirst computers at a first location, while the decompression system canbe implemented by one or more second (different) computers at a second(different) location.

In some implementations, the compression system can generate acompressed representation of an input audio waveform and store thecompressed representation in a data store, e.g., a logical data storagearea or a physical data storage device. The decompression system canlater access the compressed representation from the data store, andprocess the compressed representation to generate a corresponding outputaudio waveform. The output audio waveform can be, e.g., a reconstructionof the input audio waveform or an enhanced (e.g., de-noised) version ofthe input audio waveform.

In some implementations, the compression system can generate acompressed representation of an input audio waveform and transmit thecompressed representation to a destination over a data communicationnetwork, e.g., a local area network, a wide area network, or theinternet. The decompression system can access the compressedrepresentation at the destination, and process the compressedrepresentation to generate a corresponding output waveform.

The subject matter described in this specification can be implemented inparticular embodiments so as to realize one or more of the followingadvantages.

The compression/decompression systems described in this specificationcan enable audio data to be compressed more efficiently than someconventional systems. By enabling more efficient audio data compression,the systems allow more efficient audio data transmission (e.g., byreducing the communication network bandwidth required to transmit audiodata) and more efficient audio data storage (e.g., by reducing theamount of memory required to store audio data).

The compression/decompression systems include an encoder neural network,a set of vector quantizers, and a decoder neural network that arejointly trained (i.e., from “end-to-end”). Jointly training therespective neural network parameters of the encoder and decoder neuralnetworks along with the codebooks of the vector quantizers enables theparameters of the compression/decompression systems to be adapted inunison to achieve more efficient audio compression than would otherwisebe possible. For example, as the neural network parameters of theencoder neural network are iteratively adjusted, the codebooks of thevector quantizers are simultaneously optimized to enable more accuratequantization of the feature vectors generated by the encoder neuralnetwork. The neural network parameters of the decoder neural network arealso simultaneously optimized to enable more accurate reconstruction ofaudio waveforms from quantized feature vectors generated using theupdated codebooks of the vector quantizers.

Performing vector quantization of feature vectors representing audiowaveforms using a single vector quantizer, where each feature vector isrepresented using r bits, can require a codebook of size 2^(r). That is,the size of the codebook of the vector quantizer can increaseexponentially with the number of bits allocated to represent eachfeature vector. As the number of bits allocated to represent eachfeature vector increases, learning and storing the codebook becomescomputationally infeasible. To address this issue, thecompression/decompression systems perform vector quantization using asequence of multiple vector quantizers that each maintain a respectivecodebook. The first vector quantizer can directly quantize featurevectors generated by the encoder neural network, while each subsequentvector quantizer can quantize residual vectors that define thequantization error generated by the preceding vector quantizer.

The sequence of vector quantizers can iteratively refine thequantization of feature vectors while each maintaining a dramaticallysmaller codebook that would be required by a single vector quantizer.For example, each vector quantizer can maintain a codebook of size2^(r/N) ^(q) where r is the number of bits allocated to represent eachfeature vector and N_(q) is the number of vector quantizers. Performingvector quantization using a sequence of multiple vector quantizers thusenables the compression/decompression system to reduce the memoryrequired to store the quantizer codebooks and allows vector quantizationto be performed in situations in which doing so would otherwise becomputationally infeasible.

Performing vector quantization using a set of multiple vector quantizers(i.e., rather than a single vector quantizer) also enables thecompression/decompression systems to control the compression bitrate,e.g., the number of bits used to represent each second of audio data. Toreduce the bitrate, the compression/decompression systems can performvector quantization using fewer vector quantizers. Conversely, toincrease the bitrate, the compression/decompression systems can performvector quantization using more vector quantizers. During training, thenumber of vector quantizers used for compression/decompression of eachaudio waveform can be varied (e.g., randomly) across training examples,causing the compression/decompression systems to learn a single set ofparameter values that enable effective compression/decompression acrossa range of possible bitrates. Thus the compression/decompression systemsenable reduced consumption of computational resources by obviating anyrequirement to train and maintain multiple respective encoders,decoders, and vector quantizers that are each optimized for a respectivebitrate.

The compression/decompression systems can be trained to jointly performboth audio data compression and audio data enhancement, e.g.,de-noising. That is, the compression and decompression systems can betrained to simultaneously enhance (e.g., de-noise) an audio waveform aspart of compressing and decompressing the waveform without increasingoverall latency. In contrast, some conventional systems apply a separateaudio enhancement algorithm to an audio waveform at the transmitter side(i.e., before compression) or at the receiver side (i.e., afterdecompression) which can result in increased latency.

The details of one or more embodiments of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an example audio compression system that can compressaudio waveforms using an encoder neural network and a residual vectorquantizer.

FIG. 2 depicts an example audio decompression system that can decompresscompressed audio waveforms using a decoder neural network and a residualvector quantizer.

FIG. 3 is a schematic diagram of an example training system that canjointly train an encoder neural network, a decoder neural network and aresidual vector quantizer.

FIG. 4 is a flow diagram of an example process for compressing an audiowaveform.

FIG. 5 is a flow diagram of an example process for decompressing acompressed audio waveform.

FIG. 6 is a flow diagram of an example process for generating quantizedrepresentations of feature vectors using a residual vector quantizer.

FIG. 7 is a flow diagram of an example process for jointly training anencoder neural network, a decoder neural network and a residual vectorquantizer.

FIGS. 8A and 8B show an example of a fully convolutional neural networkarchitecture.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

FIG. 1 depicts an example audio compression system 100 that can compressaudio waveforms using an encoder neural network 102 and a residualvector quantizer 106. Similarly, FIG. 2 depicts an example audiodecompression system 200 that can decompress compressed audio waveformsusing a decoder neural network 104 and the residual vector quantizer106. For clarity, reference will be made to both FIG. 1 and FIG. 2 whendescribing various components involved in compression and decompression.The audio compression/decompression systems 100/200 are examples ofsystems implemented as computer programs on one or more computers in oneor more locations in which the systems, components, and techniquesdescribed below are implemented.

The compression/decompression systems 100/200 utilize a neural networkarchitecture (neural codec) that can outperform traditional codecs,e.g., waveform and parametric codecs, in terms of operational bitratesand general-purpose audio compression. For comparison, waveform codecstypically use time/frequency domain transforms forcompression/decompression while making little or no assumptions aboutthe source audio. As a consequence of this, they produce high-qualityaudio at mid-to-high level bitrates but tend to introduce codingartifacts at low bitrates. Parametric codecs can overcome this problemby making specific assumptions about the source audio (e.g., speech) butare ineffective for general-purpose audio compression. Conversely, theaudio compression and decompression systems 100/200 can compress anddecompress speech, music and general audio at bitrates normally targetedby speech-tailored codecs (e.g., parametric codecs). Hence, the audiocompression/decompression systems 100/200 can operate in modalities thatconventional codecs are incapable of. In some implementations, thecompression and decompression systems 100/200 can be configured forspecific types of audio content (e.g., speech) due to the flexibilityadmitted by the neural network architecture.

Referring to FIG. 1 , the compression system 100 receives an audiowaveform 112 to be compressed. The waveform 112 can include an audiosample at each time step, where the time step usually corresponds to aparticular sampling rate. Higher sampling rates capture higher frequencycomponents of the audio waveform 112. For example, the standard audiosampling rate used by professional digital equipment is 48 kHz since itcan reconstruct sound at frequencies up to 24 kHz (e.g., upper limit ofhuman hearing). Although such sampling rates are ideal for comfortablelistening, the compression system 100 can generally be configured toprocess waveforms 112 at any sampling rate, even waveforms withnon-uniform sampling.

The audio waveform 112 can originate from any suitable audio source. Forexample, the waveform 112 can be a recording from an external audiodevice (e.g., speech from a microphone), a purely digital production(e.g., electronic music), or generic audio such as sound effects andbackground noise (e.g., white noise, room tone). In someimplementations, the audio compression system 100 can perform audioenhancement, e.g., suppressing unwanted background noise, simultaneouslywhen compressing the waveform 112.

In conventional audio processing pipelines, compression and enhancementare usually performed by separate modules. For example, it is possibleto apply an audio enhancement algorithm at the input of the encoder 102,before a waveform is compressed, or at the output of the decoder 104,after the waveform is decompressed. In this setup, each processing stepcontributes to the end-to-end latency, e.g., due to buffering thewaveform to an expected frame length of the algorithm. Conversely,utilizing judicious training of various neural network components (seeFIG. 3 ), the audio compression system 100 can accomplish jointcompression and enhancement without relying on a separate module andincurring no additional latency. In some implementations, the audiodecompression system 200 implements joint decompression and enhancement.In general, the compression system 100, decompression system 200, orboth can be designed to perform audio enhancement by adequately trainingthe neural network components.

The audio waveform 112 is processed (e.g., encoded) by the encoder 102to generate a sequence of feature vectors 208 representing the waveform112. Feature vectors 208 (e.g., embeddings, latent representations) arecompressed representations of waveforms that extract the most relevantinformation about their audio content. The encoder 102 can down-samplethe input waveform 202 to generate the compressed feature vectors 208,such that the feature vectors 208 have a lower sampling rate than theoriginal audio waveform 112. For example, the encoder neural network 102can use multiple convolutional layers with increasing strides togenerate feature vectors 208 at the lower sampling rate (e.g., lowertemporal resolution).

The feature vectors 208 are then processed by a residual (e.g.,multi-stage) vector quantizer RVQ 106 to generate coded representationsof the feature vectors (CFVs) 210 and corresponding quantizedrepresentations of the feature vectors (QFVs) 212. The RVQ 106 cangenerate QFVs 212 at a particular bitrate by leveraging one or morevector quantizers 108. The RVQ 108 realizes (lossy) compression bymapping the higher-dimensional space of feature vectors 208 to adiscrete subspace of code vectors. As will be elaborated below, a CFV210 specifies codewords (e.g., indices) from respective codebooks 110 ofeach vector quantizer 108, where each codeword identifies a code vectorstored in the associated codebook 110. Consequently, a QFV 212 is anapproximation of a feature vector 208 defined by the combination of codevectors specified by the corresponding CFV 212. Generally, the QFV 212is a summation (e.g., linear combination) of code vectors specified bythe CFV 212.

In some cases, the RVQ 106 uses a single vector quantizer 108 with asingle codebook 110. The quantizer 108 can compress a feature vector 208into a QFV 212 by choosing a code vector in its codebook 110 torepresent the feature vector 208. The quantizer 106 can select the codevector based on any appropriate distance metric (e.g., error) betweenthe two vectors, e.g., L^(n)-norm, cosine distance, etc. For example,the RVQ 106 can select the code vector with the smallest Euclidean norm(e.g., L²-norm) relative to the feature vector 208. The quantizer 106can then store the corresponding codeword in a CFV 210. Since codewordsgenerally require fewer bits than code vectors, CFVs 210 consume lessspace in memory and can achieve greater compression than QFVs 212 withno additional loss.

Nevertheless, a single vector quantizer 108 approach can becomeprohibitively expensive, as the size of the codebook 110 growsexponentially as the bitrate is increased. To overcome this problem, theRVQ 106 can utilize a sequence of vector quantizers 108. In this case,each vector quantizer 108 in the sequence contains a respective codebook110 of code vectors. The RVQ 106 can then use an iterative method togenerate the CFVs 210 and corresponding QFVs 212, such that each vectorquantizer 108 in the sequence further refines quantization.

For example, at the first vector quantizer 108, the quantizer 106 canreceive the feature vector 208 and select a code vector from itscodebook 110 to represent the feature vector 208 based on a smallestdistance metric. A residual vector can be computed as the differencebetween the feature vector 208 and the code vector representing thefeature vector 208. The residual vector can be received by the nextquantizer 108 in the sequence to select a code vector from its codebook110 to represent the residual vector based on a smallest distancemetric. The difference between these two vectors can be used as theresidual vector for the next iteration. This iterative method cancontinue for each vector quantizer 108 in the sequence. Every codevector identified in the method can be summed into the QFV 212 and thecodeword of each code vector can be stored in a respective CFV 210.

In general, the RVQ 106 can utilize any suitable number of vectorquantizers 108. The number of quantizers N_(q) and the size of eachcodebook N_(i) control tradeoffs between computational complexity andcoding efficiency. Hence, a sequence of quantizers 108 provides aflexible means of balancing these two opposing factors. In some cases,the size of each codebook N_(i)=N is identical such that the total bitbudget is allocated uniformly across each vector quantizer 108. Auniform allocation provides a practical modularity to the RVQ 106 aseach codebook 110 consumes the same space in memory.

Moreover, for fixed size codebooks N_(i), the number of vectorquantizers N_(q) in the sequence determines the resulting bitrate of theQFVs 212, where higher bitrates correspond to a larger number ofquantizers 108. Thus, the RVQ 106 offers a convenient framework forvariable (e.g., scalable) bitrates by employing a structured dropout ofquantizers 108. That is, the audio compression and decompression systems100/200 can vary the number of quantizers 108 in the sequence to targetany desired bitrate, facilitating adjustable performance and reducingoverall memory footprint compared with multiple fixed bitrate codecs.Due to these capabilities, the compression/decompression systems 100/200can be particularly amendable to low latency implementations, apt fordevices with limited computing resources (e.g., smartphones, tablets,watches, etc.).

The CFVs 218 can then be further compressed, for example using anentropy codec 302, into a compressed representation of the audiowaveform 114. The entropy codec 302 can implement any appropriatelossless entropy coding, e.g., arithmetic coding, Huffman coding, etc.

Referring to FIG. 2 , the decompression system 200 receives a compressedrepresentation of an audio waveform 114. In general, the compressedaudio waveform 114 can represent any type of audio content, e.g.,speech, music, general audio, etc. Granted, as mentioned previously, theaudio compression and decompression systems 100/200 can be implementedfor specific tasks (e.g., speech-tailored compression/decompression) tooptimize around specific types of audio content.

The compressed audio waveform 114 can be decompressed into CFVs 210, forexample using the entropy codec 302. The CFVs 210 are then processed bythe RVQ 106 into QFVs 212. As described above, each CFV 210 includescodewords (e.g., indices) that identify code vectors in respectivecodebooks 110 of each vector quantizer 108. The combination of codevectors specified by each CFV 210 identifies the corresponding QFV 212.Generally, the code vectors identified by each CFV 210 are summed intothe corresponding QFV 212.

The QFVs 212 can then be processed (e.g., decoded) by the decoder 104 togenerate an audio waveform 112. The decoder 104 generally mirrors theprocesses of the encoder 102 by outputting waveforms starting from(quantized) feature vectors. The decoder 104 can up-sample the QFVs 212to generate the output waveform 206 at a higher sampling rate than theinput QFVs 212. For example, the decoder 102 can use multipleconvolutional layers with decreasing strides to generate the outputwaveform 206 at the higher sampling rate (e.g., higher temporalresolution).

Note that the compression/decompression systems 100/200 can be realizedin various different implementations such as being integrated as asingle system or as separate systems. Moreover, components of each ofthe compression/decompression systems 100/200 need not be constrained toa single client device. For example, in some implementations, thecompression system 100 stores the compressed audio waveform 114 in localstorage which is then retrieved from local storage by the decompressionsystem 200. In other implementations, the compression system 100 on atransmitter client transmits the compressed audio waveform 114 across anetwork (e.g., internet, 5G cellular network, Bluetooth, Wi-Fi, etc.)which can be received by the decompression system 200 on a receiverclient.

As will be described in more detail below, the neural networkarchitecture can be trained using a training system 300. The trainingsystem 300 can enable efficient general-purpose compression or tailoredcompression (e.g., speech-tailored) by utilizing a suitable set oftraining examples 116 and various training procedures. Specifically, thetraining system 300 can jointly train the encoder neural network 102 anddecoder neural network 104 to efficiently encode and decode featurevectors 208 of various waveforms contained in the training examples 116.Furthermore, the training system 300 can train the RVQ 106 toefficiently quantize the feature vectors 208. In particular, eachcodebook 110 of each cascading vector quantizer 108 can be trained tominimize quantization error. To facilitate trainable codebooks 110, eachvector quantizer 108 can, for example, be realized as a vector quantizedvariational autoencoder (VQ-VAE).

The audio compression/decompression systems 100/200 can be a fully“end-to-end” machine learning approach when implementing thisdata-driven training solution. In the end-to-end implementation, thecompression/decompression systems 100/200 leverage the neural networksfor all tasks involved in training, as well as inference after training.No processing, such as feature extraction, is performed by an externalsystem. In general, the training system 300 can utilize unsupervisedlearning algorithms, semi-supervised learning algorithms, supervisedlearning algorithms, or more elaborate combinations of these. Forexample, the training system 300 can balance reconstruction losses withadversarial losses to enable audio compression that is both faithful andperceptually similar to the original audio on playback.

Generally, the neural networks included in the audiocompression/decompression systems 100/200 can have any appropriateneural network architectures which enable them to perform theirdescribed functions. In particular, the neural networks can each includeany appropriate neural network layers (e.g., fully-connected layer,convolutional layers, attention layers, etc.) in any appropriate numbers(e.g., 5, 10, or 100 layers) and arranged in any appropriateconfiguration (e.g., as a linear sequence of layers).

In some implementations, the compression/decompression systems 100/200exploit a fully convolutional neural network architecture. FIGS. 8A and8B show an example implementation of such an architecture for theencoder 102 and decoder 104 neural networks. A fully convolutionalarchitecture can be particularly advantageous for low latencycompression since it has a lower scale connectivity compared tofully-connected networks (e.g., multilayer perceptrons) and has filters(e.g., kernels) that can be optimized to limit coding artifacts.Moreover, convolutional neural networks provide an effective means ofresampling the waveform 112, i.e., changing the temporal resolution ofthe waveform 112, by using different strides for different convolutionallayers.

In further implementations, the compression/decompression systems100/200 use strictly causal convolutions when implementing a fullyconvolutional architecture, such that padding is only applied to thepast but not the future in both training and offline inference. Nopadding is necessary for streaming inference. In this case, the overalllatency of the compression and decompressions systems 100/200 isdetermined entirely by the temporal resampling ratio between waveformsand their corresponding feature vectors.

FIG. 3 shows operations performed by an example training system 300 tojointly train an encoder neural network 102, a decoder neural network104 and a residual vector quantizer 106. The neural networks are trainedend-to-end on an objective function 214 that can include numerousreconstruction losses. In some implementations, a discriminator neuralnetwork 216 is also trained to facilitate adversarial losses 218 and, insome cases, additional reconstruction losses.

The training system 300 receives a set of training examples 116. Eachtraining example 116 includes a respective input audio waveform 202 anda corresponding target audio waveform 204 that the neural networks aretrained to reconstruct. That is, using the objective function 214, thetarget waveform 204 can be compared with a resulting output audiowaveform 206 to evaluate performance of the neural networks.Specifically, the objective function 214 can include a reconstructionloss that measures an error between the target waveform 204 and theoutput waveform 206. In some cases, a point-wise reconstruction loss onthe raw waveforms is implemented, for example, using a mean squarederror between the waveforms.

However, this type of reconstruction loss may have limitations incertain cases, e.g., because two distinct waveforms can soundperceptually identical, while point-wise similar waveforms can soundvery different. To alleviate this problem, the objective function 214can utilize a multi-scale spectral reconstruction loss that measures anerror between mel-spectrograms of the target waveform 204 and the outputwaveform 206. A spectrogram characterizes the frequency spectrum of anaudio waveform over time, e.g., using a short-time Fourier transform(STFT). A mel-spectrogram is a spectrogram converted to mel-scale. Sincehumans generally do not perceive sound frequencies on a linear scale,the mel-scale can appropriately weigh frequency components to promotefidelity. For example, the reconstruction loss

_(rec) between the target waveform {tilde over (x)} and the outputwaveform {tilde over (x)} can include terms that measure an absoluteerror and a log error of mel-spectrograms,

$\mathcal{L}_{rec} = {\sum\limits_{{s \in 2^{6}},\ldots,2^{11}}{\sum\limits_{t}\left( {{{{S_{t}^{s}\left( \overset{\sim}{x} \right)} - {S_{t}^{s}\left( \hat{x} \right)}}}_{1} + {\alpha_{s}{{{\log{S_{t}^{s}\left( \overset{\sim}{x} \right)}} - {\log{S_{t}^{s}\left( \hat{x} \right)}}}}_{2}}} \right)}}$

where ∥ . . . ∥_(n) indicates the L^(n)-norm. Although otherreconstructions losses are possible, this form of

_(rec) satisfies a strictly proper scoring rule which can be desirablefor training purposes. Here, S_(t) ^(s) denotes the t-th frame (e.g.,timeslice) of a 64-bin mel-spectrogram computed with window length equalto s and hop length equal to s/4. The α_(s) coefficient can be set toα_(s)=√{square root over (s/2)}.

As mentioned previously, the set of training examples 116 can beselected to enable various modalities of the compression/decompressionsystems 100/200, such as general-purpose audio compression,speech-tailored compression, etc. For example, to train forgeneral-purpose audio compression, the training examples 116 can includespeech, music, and general audio waveforms. In other implementations,the training examples 116 may only include music waveforms to facilitateoptimal music compression and playback.

In some cases, the target waveform 204 is identical to the inputwaveform 202, which can train the neural networks towards faithful andperceptually similar reconstructions. However, the target waveform 204can also be modified with respect to the input waveform 202 to encouragemore sophisticated functionalities, such as joint compression andenhancement. The nature of the enhancement can be determined bydesigning training examples 116 with certain qualities. For instance,the target waveform 204 can be a speech enhanced version of the inputwaveform 202, such that the neural networks improve audio dialogue uponreconstruction of waveforms. Alternatively or in addition, the targetwaveform 204 can be a denoised version of the input waveform 202, whichtrains the networks to suppress background noise. In general, anydesired audio enhancement can be enabled using this technique.

In further implementations, the encoder 102 and/or decoder 104 can beconditioned on data, usually included in the training examples 116, thatdefines whether the target waveform 204 is identical to the inputwaveform 202 or is an enhanced version of the waveform 202. Forinstance, the training examples 116 can include a conditioning signalthat represents the two modes (enhancement enabled or disabled), suchthat the neural networks are trained to only enable enhancement when thesignal is present. To implement this, the encoder 102 and/or decoder 104can have a dedicated layer, such as a Feature-wise Linear Modulation(FilM) layer, to process the conditioning signal. After training, thistechnique can allow the audio compression/decompression systems 100/200to flexibly control enhancement in real-time by feeding the conditioningsignal through the network. Accordingly, the compression system 100 canimplement this controllable enhancement to permit compression ofacoustic scenes and natural sounds that would be otherwise removed byenhancement (e.g., denoising).

Returning now to the encoder neural network 102. The input waveform 202is processed by the encoder 102 and encoded into a sequence of featurevectors 208. This process, that may involve numerous encoder networklayers, can be collectively represented by an encoder function ϵ_(θ)that maps the input waveform x to the feature vectors y, such thaty(x)=ϵ_(θ)(x). The encoder function ϵ_(θ) is parametrized by encodernetwork parameters θ which can be updated using the objective function214 to minimize losses during encoding.

The feature vectors 208 are then compressed by the RVQ 106 to generatecoded CFVs 210 and corresponding QFVs 212. Note that the quantizationprocess of the RVQ 106, which may involve numerous vector quantizers108, can be collectively represented by a RVQ function

_(ψ) that maps the feature vectors y to the QFVs ŷ, such that ŷ(x)=

_(ψ)(y)=

_(ψ)(ϵ_(θ)(x)). The RVQ function

_(ψ) is parametrized by codebook parameters which can be updated usingthe objective function 214 to minimize losses during quantization.

The training system 300 can minimize the quantization loss associatedwith the RVQ 106 by properly aligning the code vectors with the vectorspace of feature vectors 208. That is, the codebook parameters ψ can beupdated by the training system 300 by backpropagating gradients of theobjective function 214. For example, the codebooks 110 can be repeatedlyupdated during training using exponential moving averages of the featurevectors 208. The training system 300 can also improve usage of thecodebooks 110 by running a k-means algorithm on a first set of trainingexamples 116 and using the learned centroids as initialization for thefollowing training examples 116. Alternatively or in addition, if a codevector has not been assigned to a feature vector 208 for numeroustraining examples 116, the training system 300 can replace it with arandom feature vector 208 sampled during a current training example 116.For example, the training system 300 can track the exponential movingaverage of assignments to each code vector (with a decay factor of 0.99)and replace the code vectors of which this statistic falls below 2.

To adequately train the neural networks for variable (e.g., scalable)bit rates, the training system 300 can select a particular number n_(q)of vector quantizers 108 to be used for each training example 116, suchthat the number of quantizers 108 differs between training examples 116.For instance, the training system 300 can sample n_(q) uniformly atrandom in [1; N_(q)], for each training example 116, and only use thefirst i=1 . . . n_(q) quantizers 108 in the sequence. Consequently, thenetworks are trained to encode and decode audio waveforms for all targetbitrates corresponding to the range n_(q)=1. . . N_(q) and noarchitectural changes are necessary for the encoder 102 or decoder 104.After training, the audio compression and decompression systems 100/200can select a particular number of quantizers n_(q) during compressionand decompression which accommodates a desired bitrate.

Referring now to the decoder neural network 104. The QFVs 212 areprocessed by the decoder 104 and decoded into the output audio waveform206. Analogous to the encoder 102, decoding may involve numerous decodernetwork layers, that can be collectively represented by a decoderfunction

_(ϕ). The decoder function

_(ϕ) maps the input QFVs ŷ to the output waveform {circumflex over (x)},such that {circumflex over (x)}(x)=

_(ϕ)(ŷ)=

_(φ)(

_(ψ)(ϵ_(θ)(x))). In some implementations, the input waveform x and theoutput waveform 2 have the same sampling rate, but this need not be thecase. The decoder function

_(ϕ) is parametrized by decoder network parameters ϕ which can beupdated using the objective function 214 to minimize losses duringdecoding.

Since the output waveform {circumflex over (x)} generally depends onencoder network parameters θ, codebook parameters ψ and decoder networkparameters ϕ, the objective function 214, which includes reconstructionlosses between the output waveform 206 and the target waveform 204 ofeach training example 116, can be used to update these networkparameters. Specifically, gradients of the objective function 214 can becomputed to iteratively update the network parameters withbackpropagation, e.g., using a gradient descent method. Generally, thenetwork parameters are updated with the goal of optimizing the objectivefunction 214.

In some implementations, the training system 300 exploits adiscriminator neural network 216 to incorporate adversarial loss 218into the objective function 214, and potentially additionalreconstruction losses. The adversarial loss 218 can promote perceptualquality of waveforms reconstructed by the neural networks. In this case,the discriminator 216 is jointly trained by the training system 300 andcontests with the encoder 102, decoder 104, and RVQ 106. That is, thediscriminator 216 is trained to distinguish target waveforms 204 fromoutput waveforms 206 while the encoder 102, decoder 104 and RVQ 106 aretrained to fool the discriminator 216.

The discriminator 216 can implement this into the adversarial loss 218by using a set of discriminator scores

_(k) with k={1,2, . . . , K}, such that each score characterizes anestimated likelihood that the output waveform 206 is not generated asoutput from the decoder 104. For example, the discriminator 216 canreceive the output waveform {circumflex over (x)} from the decoder 104and process the waveform using one or more neural network layers togenerate logits

_(k,t)({circumflex over (x)}). In this case

_(k,t) is a discriminator function that maps an input waveform to outputlogits. k indexes a particular discriminator output and t indexes aparticular logit of the discriminator output. In some implementations,the discriminator 216 utilizes a fully convolutional neural network suchthat the number of logits is proportional to the length of the inputwaveform.

The discriminator 216 can use the logits to determine the respectivediscriminator scores

_(k) for each discriminator output k. For example, each score

_(k) can be determined from the average over logits as,

$\mathcal{L}_{k} = {E_{x}\left\lbrack {\frac{1}{T_{k}}{\sum\limits_{t}{\max\left\lbrack {0,{1 - {\mathcal{G}_{k,t}\left( {\hat{x}(x)} \right)}}} \right\rbrack}}} \right\rbrack}$

Here, T_(k) is the total number of logits for the output k and E_(x) isthe expected value over x.

In some implementations, the adversarial loss

_(adv) is an average over the discriminator scores

_(k),

$\mathcal{L}_{adv} = {\frac{1}{K}{\sum\limits_{k}\mathcal{L}_{k}}}$

The adversarial loss

_(adv) can be included in the objective function 214 to promoteperceptual quality of reconstructed waveforms. Moreover, thediscriminator 216 can be trained by the training system 300 todistinguish target waveforms {tilde over (x)} from output waveforms{circumflex over (x)} by minimizing a discriminator loss function

_(dis). In some implementations,

_(dis) has the form,

$\mathcal{L}_{dis} = {{\frac{1}{K}{\sum\limits_{k}{E_{x}\left\lbrack {\frac{1}{T_{k}}{\sum\limits_{t}{\max\left\lbrack {0,{1 - {\mathcal{G}_{k,t}\left( {\overset{\sim}{x}(x)} \right)}}} \right\rbrack}}} \right\rbrack}}} + {\frac{1}{K}{\sum\limits_{k}{E_{x}\left\lbrack {\frac{1}{T_{k}}{\sum\limits_{t}{\max\left\lbrack {0,{1 + {\mathcal{G}_{k,t}\left( {\hat{x}(x)} \right)}}} \right\rbrack}}} \right\rbrack}}}}$

Note, target waveforms {tilde over (x)}(x) generally depend on inputwaveforms x in that they can be identical to the input waveform {tildeover (x)}(x)=x or an enhanced version. By training the discriminator 216to efficiently classify target waveforms 204 from output waveforms 206with respect to

_(dis), the encoder 102, decoder 104, and RVQ 106 learn to fool thediscriminator by minimizing

_(adv).

In some implementations, the discriminator 216 exploits differentversions of the waveforms to determine the discriminator scores

_(k). For example, besides the original waveforms, the discriminator 216can also use down-sampled versions of the waveforms (e.g., 2-timesdown-sampled, 4-times down-sampled, etc.) or Fourier-transformedversions of the waveforms (e.g., STFT, Hartley transform, etc.) whichadds diversity to the adversarial loss 218. As a particularimplementation using four discriminator scores, the

_(k=1) score can correspond to a STFT waveform, while discriminatorscores

_(k=2,3,4) can correspond to an original waveform, a 2-timesdown-sampled waveform and a 4-times down-sampled waveform.

In further implementations, the discriminator 216 introduces areconstruction loss in the form of a “feature loss”. Specifically, thefeature loss

_(feat) measures an error between the discriminator's internal layeroutputs for the target audio waveform 204 and those for the output audiowaveform 206. For example, the feature loss

_(feat) can be expressed as the absolute difference betweendiscriminator outputs

_(k,t) ^((l)) for the target waveform {tilde over (x)} and outputwaveform {tilde over (x)} for each layer l∈{1,2, . . . , L} as,

$\mathcal{L}_{feat} = {E_{x}\left\lbrack {\frac{1}{KL}{\sum\limits_{k,l}{\frac{1}{T_{k,l}}{\sum\limits_{t}{❘{{\mathcal{G}_{k,t}^{(l)}\left( {\overset{\sim}{x}(x)} \right)} - {\mathcal{G}_{k,t}^{(l)}\left( {\hat{x}(x)} \right)}}❘}}}}} \right\rbrack}$

The feature loss can be a useful tool to promote increased fidelitybetween the output waveform 206 and the target waveform 204. Taking intoaccount all the aforementioned loss terms, the objective function

can control tradeoffs between reconstruction losses, adversarial losses,as well as feature losses,

=λ_(rec)

_(rec)+λ_(adv)

_(adv)+λ_(feat)

_(feat)

By weighting appropriate loss terms with weight factors λ_(rec), λ_(adv)and λ_(feat), the objective function 214 can emphasize certainproperties, such as faithful reconstructions, fidelity, perceptualquality, etc. In some implementations, the weight factors are set toλ_(rec)=λ_(adv)=1 and λ_(feat)=100.

FIG. 4 is a flow diagram of an example process 400 for compressing anaudio waveform. For convenience, the process 400 will be described asbeing performed by a system of one or more computers located in one ormore locations. For example, an audio compression system, e.g., theaudio compression system 100 of FIG. 1 , appropriately programmed inaccordance with this specification, can perform the process 400.

The system receives an audio waveform (402). The audio waveform includesa respective audio sample at each of a plurality of time steps. In somecases, the time steps may correspond to a particular sampling rate.

The system processes the audio waveform using an encoder neural networkto generate feature vectors (404) representing the audio waveform.

The system processes each feature vector using a plurality of vectorquantizers to generate respective coded representations of the featurevectors (406), where each vector quantizer is associated with arespective codebook of code vectors. Each coded representation of afeature vector identifies a plurality of code vectors, including a codevector from the codebook of each vector quantizer, which define arespective quantized representation of the feature vector. In someimplementations, the respective quantized representation of the featurevector is defined by a sum of the plurality of code vectors.

The system compresses the coded representations of the feature vectorsto generate a compressed representation of the audio waveform (408). Insome implementations, the system compresses the coded representations ofthe feature vectors using entropy encoding.

FIG. 5 is a flow diagram of an example process 500 for decompressing acompressed audio waveform. For convenience, the process 500 will bedescribed as being performed by a system of one or more computerslocated in one or more locations. For example, an audio decompressionsystem, e.g., the audio decompression system 200 of FIG. 2 ,appropriately programmed in accordance with this specification, canperform the process 500.

The system receives a compressed representation of an input audiowaveform (502).

The system decompresses the compressed representation of the audiowaveform to obtain coded representations of feature vectors representingthe input audio waveform (504). In some implementations, the systemdecompresses the compressed representation of the input audio waveformusing entropy decoding.

The system identifies, for each coded representation of the featurevectors, a plurality of code vectors, including a code vector from thecodebook of each vector quantizer, that define a respective quantizedrepresentation of the feature vector (506). In some implementations, therespective quantized representation of the feature vector is defined bya sum of the plurality of code vectors.

The system processes the quantized representations of the featurevectors using a decoder neural network to generate an output audiowaveform (510). The output audio waveform may include a respective audiosample at each of a plurality of time steps. In some cases, the timesteps may correspond to a particular sampling rate.

FIG. 6 is a flow diagram of an example process 600 for generatingquantized representations of feature vectors using a residual vectorquantizer. For convenience, the process 600 will be described as beingperformed by a system of one or more computers located in one or morelocations.

The system receives a feature vector at a first vector quantizer in asequence of vector quantizers (602).

The system identifies, based on the feature vector, a code vector from acodebook of the first vector quantizer in the sequence to represent thefeature vector (604). For example, a distance metric (e.g., error) canbe computed between the feature vector and each code vector in thecodebook. The code vector with the smallest distance metric can beselected to represent the feature vector.

The system determines a current residual vector based on an errorbetween the feature vector and the code vector that represents thefeature vector (606). For example, the residual vector can be thedifference between the feature vector and the code vector thatrepresents the feature vector. A codeword corresponding to the codevector that represents the feature vector can be stored in a codedrepresentation of the feature vector.

The system receives the current residual vector generated by a precedingvector quantizer in the sequence at a next vector quantizer in thesequence (608).

The system identifies, based on the current residual vector, a codevector from a codebook of the next vector quantizer in the sequence torepresent the current residual vector (610). For example, a distancemetric (e.g., error) can be computed between the current residual vectorand each code vector in the codebook. The code vector with the smallestdistance metric can be selected to represent the current residualvector. A codeword corresponding to the code vector that represents thecurrent residual vector can be stored in the coded representation of thefeature vector.

The system updates the current residual vector based on an error betweenthe current residual vector and the code vector that represents thecurrent residual vector (612). For example, the current residual vectorcan be updated by subtracting the code vector that represents thecurrent residual vector from the current residual vector.

Steps 606-612 can be repeated for each remaining vector quantizer in thesequence. The final coded representation of the feature vector containsthe codeword of each code vector selected from its respective codebookduring the process 600. A quantized representation of the feature vectorcorresponds to the summation of all code vectors specified by thecodewords of the coded representation of the feature vector. In someimplementations, the codebooks of the vector quantizers in the sequenceinclude an equal number of code vectors such that each codebook isallocated the same space in memory.

FIG. 7 is a flow diagram of an example process 700 for jointly trainingan encoder neural network, a decoder neural network and a residualvector quantizer. For convenience, the process 700 will be described asbeing performed by a system of one or more computers located in one ormore locations. For example, a training system, e.g., the trainingsystem 300 of FIG. 3 , appropriately programmed in accordance with thisspecification, can perform the process 700.

The system obtains training examples that include a respective inputaudio waveform and a corresponding target audio waveform (702). In someimplementations, the target audio waveform of one or more of thetraining examples can be an enhanced version of the input audiowaveform, such as a denoised version of the input audio waveform. Thetarget audio waveform of one or more of the training examples can alsobe the same as the input audio waveform. Alternatively or in addition,the input audio waveform can be a speech or music waveform.

The system processes the input audio waveform for each training exampleusing an encoder neural network, a plurality of vector quantizers, and adecoder neural network to generate a respective output audio waveform(704), where each vector quantizer is associated with a respectivecodebook. In some implementations, the encoder and/or decoder neuralnetworks are conditioned on data that defines where the correspondingtarget audio waveform is the same as the input audio waveform or anenhanced version of the input audio waveform.

The system determines gradients of an objective function, e.g., usingbackpropagation, that depends on the respective output and target audiowaveforms for each training example (706).

The system uses the gradients of the objective function to update one ormore of: a set of encoder network parameters, a set of decoder networkparameters, or the codebooks of the plurality of vector quantizers(708). For example, the parameters can be updated using an update ruleof any appropriate gradient descent optimization technique, e.g.,RMSprop, Adam, etc.

FIGS. 8A and 8B show an example of a fully convolutional neural networkarchitecture for the encoder 102 and decoder 104 neural networks. Crepresents the number of channels and D is the dimensionality of thefeature vectors 208. The architecture in FIGS. 8A and 8B is based on theSoundStream model developed by N. Zeghidour, A. Luebs, A. Omran, J.Skoglund and M. Tagliasacchi, “SoundStream: An End-to-End Neural AudioCodec,” in IEEE/ACM Transactions on Audio, Speech, and LanguageProcessing, vol. 30, pp. 495-507, 2022. This model is an adaptation ofthe SEANet encoder-decoder network, but without skip connections,designed by Y. Li, M. Tagliasacchi, O. Rybakov, V. Ungureanu and D.Roblek, “Real-Time Speech Frequency Bandwidth Extension,” ICASSP2021-2021 IEEE International Conference on Acoustics, Speech and SignalProcessing (ICASSP), 2021, pp. 691-695.

The encoder 102 includes a ConvlD layer 802 followed by fourEncoderBlocks 804. Each of the blocks includes three ResidualUnits 812,containing dilated convolutions with dilation rates of 1, 3, and 9,respectively, followed by a down-sampling layer in the form of a stridedconvolution. Internal convolutional layers of EncoderBlocks 804 andResidualUnits 812 are shown in FIG. 8B. The number of channels isdoubled whenever down-sampling. A final ConvlD layer 802 with a kernelof length 3 and a stride of 1 is used to set the dimensionality of thefeature vectors 208 to D. A FiLM conditioning layer 806 can also beimplemented to process a conditioning signal for use in jointcompression and enhancement. The FiLM layer 806 carries out afeature-wise affine transformation on the neural network's featurevectors 208, conditioned on the conditioning signal.

In this case, the decoder 104 effectively mirrors the encoder 102. TheDecoderBlocks 810 include a transposed ConvlD layer 814 for up-samplingfollowed by three ResidualUnits 812. Internal convolutional layers ofDecoderBlocks 810 and ResidualUnits 812 are shown in FIG. 8B. Thedecoder 104 uses the same strides as the encoder 102, but in reverseorder, to reconstruct a waveform with the same resolution as the inputwaveform. The number of channels is halved whenever up-sampling. A finalConvlD layer 802 with one filter, a kernel of size 7 and stride 1projects the feature vectors 208 back to the waveform 112. A FiLMconditioning layer 806 can also be implemented to process theconditioning signal for joint decompression and enhancement. In someimplementations, both the encoder 102 and decoder 104 perform audioenhancement, while in other implementations only one of the encoder 102or decoder 104 is responsible.

This specification uses the term “configured” in connection with systemsand computer program components. For a system of one or more computersto be configured to perform particular operations or actions means thatthe system has installed on it software, firmware, hardware, or acombination of them that in operation cause the system to perform theoperations or actions. For one or more computer programs to beconfigured to perform particular operations or actions means that theone or more programs include instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the operations oractions.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non-transitory storage medium for execution by, or to controlthe operation of, data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them. Alternatively or in addition, the programinstructions can be encoded on an artificially-generated propagatedsignal, e.g., a machine-generated electrical, optical, orelectromagnetic signal, that is generated to encode information fortransmission to suitable receiver apparatus for execution by a dataprocessing apparatus.

The term “data processing apparatus” refers to data processing hardwareand encompasses all kinds of apparatus, devices, and machines forprocessing data, including by way of example a programmable processor, acomputer, or multiple processors or computers. The apparatus can alsobe, or further include, special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application-specificintegrated circuit). The apparatus can optionally include, in additionto hardware, code that creates an execution environment for computerprograms, e.g., code that constitutes processor firmware, a protocolstack, a database management system, an operating system, or acombination of one or more of them.

A computer program, which may also be referred to or described as aprogram, software, a software application, an app, a module, a softwaremodule, a script, or code, can be written in any form of programminglanguage, including compiled or interpreted languages, or declarative orprocedural languages; and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A program may, but neednot, correspond to a file in a file system. A program can be stored in aportion of a file that holds other programs or data, e.g., one or morescripts stored in a markup language document, in a single file dedicatedto the program in question, or in multiple coordinated files, e.g.,files that store one or more modules, sub-programs, or portions of code.A computer program can be deployed to be executed on one computer or onmultiple computers that are located at one site or distributed acrossmultiple sites and interconnected by a data communication network.

In this specification the term “engine” is used broadly to refer to asoftware-based system, subsystem, or process that is programmed toperform one or more specific functions. Generally, an engine will beimplemented as one or more software modules or components, installed onone or more computers in one or more locations. In some cases, one ormore computers will be dedicated to a particular engine; in other cases,multiple engines can be installed and running on the same computer orcomputers.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby special purpose logic circuitry, e.g., an FPGA or an ASIC, or by acombination of special purpose logic circuitry and one or moreprogrammed computers.

Computers suitable for the execution of a computer program can be basedon general or special purpose microprocessors or both, or any other kindof central processing unit. Generally, a central processing unit willreceive instructions and data from a read-only memory or a random accessmemory or both. The essential elements of a computer are a centralprocessing unit for performing or executing instructions and one or morememory devices for storing instructions and data. The central processingunit and the memory can be supplemented by, or incorporated in, specialpurpose logic circuitry. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto-optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer-readable media suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto-optical disks; andCD-ROM and DVD-ROM disks.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's device in response to requests received from the web browser.Also, a computer can interact with a user by sending text messages orother forms of message to a personal device, e.g., a smartphone that isrunning a messaging application, and receiving responsive messages fromthe user in return.

Data processing apparatus for implementing machine learning models canalso include, for example, special-purpose hardware accelerator unitsfor processing common and compute-intensive parts of machine learningtraining or production, i.e., inference, workloads.

Machine learning models can be implemented and deployed using a machinelearning framework, e.g., a TensorFlow framework.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back-end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front-end component, e.g., aclient computer having a graphical user interface, a web browser, or anapp through which a user can interact with an implementation of thesubject matter described in this specification, or any combination ofone or more such back-end, middleware, or front-end components. Thecomponents of the system can be interconnected by any form or medium ofdigital data communication, e.g., a communication network. Examples ofcommunication networks include a local area network (LAN) and a widearea network (WAN), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other. In someembodiments, a server transmits data, e.g., an HTML page, to a userdevice, e.g., for purposes of displaying data to and receiving userinput from a user interacting with the device, which acts as a client.Data generated at the user device, e.g., a result of the userinteraction, can be received at the server from the device.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or on the scope of what may be claimed, but rather asdescriptions of features that may be specific to particular embodimentsof particular inventions. Certain features that are described in thisspecification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be describedabove as acting in certain combinations and even initially be claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings and recited inthe claims in a particular order, this should not be understood asrequiring that such operations be performed in the particular ordershown or in sequential order, or that all illustrated operations beperformed, to achieve desirable results. In certain circumstances,multitasking and parallel processing may be advantageous. Moreover, theseparation of various system modules and components in the embodimentsdescribed above should not be understood as requiring such separation inall embodiments, and it should be understood that the described programcomponents and systems can generally be integrated together in a singlesoftware product or packaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In some cases, multitasking and parallel processing may beadvantageous.

What is claimed is:
 1. A method performed by one or more computers, themethod comprising: receiving a compressed representation of an audiowaveform; decompressing the compressed representation of the audiowaveform to obtain a respective coded representation of each of aplurality of feature vectors representing the audio waveform, whereinthe coded representation of each feature vector identifies a pluralityof code vectors, including a respective code vector from a respectivecodebook of each of a plurality of vector quantizers, that define aquantized representation of the feature vector; generating a respectivequantized representation of each feature vector from the codedrepresentation of the feature vector; and processing the quantizedrepresentations of the feature vectors using a decoder neural network togenerate an output audio waveform.
 2. The method of claim 1, wherein theplurality of vector quantizers are ordered in a sequence and configuredto, for each of the plurality of feature vectors, generate the codedrepresentation of the feature vector, the generating comprising: for afirst vector quantizer in the sequence of vector quantizers: receivingthe feature vector; identifying, based on the feature vector, arespective code vector from the codebook of the vector quantizer torepresent the feature vector; and determining a current residual vectorbased on an error between: (i) the feature vector, and (ii) the codevector that represents the feature vector; wherein the codedrepresentation of the feature vector identifies the code vector thatrepresents the feature vector.
 3. The method of claim 2, wherein foreach of the plurality of feature vectors, generating the codedrepresentation of the feature vector further comprises: for each vectorquantizer after the first vector quantizer in the sequence of vectorquantizers: receiving a current residual vector generated by a precedingvector quantizer in the sequence of vector quantizers; identifying,based on the current residual vector, a respective code vector from thecodebook of the vector quantizer to represent the current residualvector; and if the vector quantizer is not a last vector quantizer inthe sequence of vector quantizers: updating the current residual vectorbased on an error between: (i) the current residual vector, and (ii) thecode vector that represents the current residual vector; wherein thecoded representation of the feature vector identifies the code vectorthat represents the current residual vector.
 4. The method of claim 1,wherein decompressing the compressed representation of the audiowaveform to obtain the respective coded representation of each of theplurality of feature vectors comprises: entropy decoding a respectiveentropy encoded representation of each of the coded representations ofthe feature vectors.
 5. The method of claim 1, wherein the respectivequantized representation of each feature vector is defined by a sum ofthe plurality of code vectors identified by the coded representation ofthe feature vector.
 6. The method of claim 1, wherein the codebooks ofthe plurality of vector quantizers all include an equal number of codevectors.
 7. The method of claim 1, wherein the decoder neural networkand the codebooks of the plurality of vector quantizers are jointlytrained along with an encoder neural network, wherein the encoder neuralnetwork is configured to: receive an input audio waveform that comprisesa respective audio sample for each of a plurality of time steps; andprocess the input audio waveform to generate a plurality of featurevectors representing the input audio waveform.
 8. The method of claim 7,wherein the training comprises: obtaining a plurality of trainingexamples that each include: (i) a respective input audio waveform, and(ii) a corresponding target audio waveform; processing the respectiveinput audio waveform from each training example using the encoder neuralnetwork, a plurality of vector quantizers from a sequence of vectorquantizers, and the decoder neural network to generate an output audiowaveform for the training example that is an estimate of thecorresponding target audio waveform; determining gradients of anobjective function that depends on the respective output and targetwaveforms for each training example; and using the gradients of theobjective function to update one or more of: a set of encoder neuralnetwork parameters, a set of decoder neural network parameters, or thecodebooks of the plurality of vector quantizers.
 9. The method of claim8, wherein for one or more of the training examples, the target audiowaveform is an enhanced version of the input audio waveform.
 10. Themethod of claim 9, wherein for one or more of the training examples, thetarget audio waveform is a de-noised version of the input audiowaveform.
 11. The method of claim 9, wherein for one or more of thetraining examples, the target audio waveform is the same as the inputaudio waveform.
 12. The method of claim 11, wherein processing eachinput audio waveform to generate the corresponding output audio waveformcomprises: conditioning the encoder neural network, the decoder neuralnetwork, or both, on data that defines whether the corresponding targetaudio waveform is: (i) the input audio waveform or (ii) an enhancedversion of the input audio waveform.
 13. The method of claim 8, furthercomprising, for each training example: selecting a respective number ofvector quantizers to be used in quantizing feature vectors representingthe input audio waveform; and generating the corresponding output audiowaveform using only the selected number of vector quantizers from thesequence of vector quantizers.
 14. The method of claim 13, wherein theselected number of vector quantizers to be used in quantizing featurevectors representing input audio waveforms varies between trainingexamples.
 15. The method of claim 13, wherein for each training example,selecting the respective number of vector quantizers to be used inquantizing feature vectors representing the input audio waveformcomprises: randomly sampling the number of vector quantizers to be usedin quantizing feature vectors representing the input audio waveform. 16.The method of claim 8, wherein the objective function comprises areconstruction loss that, for each training example, measures an errorbetween: (i) the output audio waveform, and (ii) the correspondingtarget audio waveform.
 17. The method of claim 16, wherein for eachtraining example, the reconstruction loss measures a multi-scalespectral error between: (i) the output audio waveform, and (ii) thecorresponding target audio waveform.
 18. The method of claim 8, whereinthe training further comprises, for each training example: processingdata derived from the output audio waveform using a discriminator neuralnetwork to generate a set of one or more discriminator scores, whereineach discriminator score characterizes an estimated likelihood that theoutput audio waveform is an audio waveform that was generated using theencoder neural network, the plurality of vector quantizers, and thedecoder neural network; wherein the objective function comprises anadversarial loss that depends on the discriminator scores generated bythe discriminator neural network.
 19. A system comprising: one or morecomputers; and one or more storage devices communicatively coupled tothe one or more computers, wherein the one or more storage devices storeinstructions that, when executed by the one or more computers, cause theone or more computers to perform operations comprising: receiving acompressed representation of an audio waveform; decompressing thecompressed representation of the audio waveform to obtain a respectivecoded representation of each of a plurality of feature vectorsrepresenting the audio waveform, wherein the coded representation ofeach feature vector identifies a plurality of code vectors, including arespective code vector from a respective codebook of each of a pluralityof vector quantizers, that define a quantized representation of thefeature vector; generating a respective quantized representation of eachfeature vector from the coded representation of the feature vector; andprocessing the quantized representations of the feature vectors using adecoder neural network to generate an output audio waveform.
 20. One ormore non-transitory computer storage media storing instructions thatwhen executed by one or more computers cause the one or more computersto perform operations comprising: receiving a compressed representationof an audio waveform; decompressing the compressed representation of theaudio waveform to obtain a respective coded representation of each of aplurality of feature vectors representing the audio waveform, whereinthe coded representation of each feature vector identifies a pluralityof code vectors, including a respective code vector from a respectivecodebook of each of a plurality of vector quantizers, that define aquantized representation of the feature vector; generating a respectivequantized representation of each feature vector from the codedrepresentation of the feature vector; and processing the quantizedrepresentations of the feature vectors using a decoder neural network togenerate an output audio waveform.